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Mathematical Physics Seminar

David Nelson - The Statistical Mechanics of Mutilated Sheets and Shells

David Nelson

Location:  Webinar
Date & time: Thursday, 16 July 2020 at 11:00AM - 12:00PM



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David Nelson – Harvard University

Thursday, July 16, 11:00AM


"The Statistical Mechanics of Mutilated Sheets and Shells”

Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904, a precursor of general relativity characterized by a dimensionless coupling constant (the "Foeppl-von Karman number") that can easily reach  vK = 10^7 in an ordinary sheet of writing paper.  However, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics, as exemplified by experiments that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 10^13!)   We will discuss recent results for the bending and pulling of thermalized graphene ribbons, and then move on to analyze thin amorphous spherical shells with a uniform nonzero curvature, accessible for example with soft matter experiments on diblock copolymers.  This curvature couples the in-plane stretching modes with the out-of-plane undulation modes, giving rise to qualitative differences in the fluctuations of thermal spherical shells (and hollow cylinders) compared to flat membranes.    These expectations are confirmed by extensive molecular dynamics simulations, suggesting that, using free-standing graphene sheets, it may be possible to study the quantum mechanics of two dimensional Dirac massless fermions in a fluctuating curved space whose dynamics resembles a simplified form of general relativity.

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